Question: Simplify; express your answer in exponential form. Assume $z\neq 0, a\neq 0$. $\dfrac{{(z^{-4})^{-2}}}{{z^{-5}a^{2}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${z^{-4}}$ to the exponent ${-2}$ . Now ${-4 \times -2 = 8}$ , so ${(z^{-4})^{-2} = z^{8}}$ In the denominator, we can use the distributive property of exponents. ${z^{-5}a^{2} = z^{-5}a^{2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(z^{-4})^{-2}}}{{z^{-5}a^{2}}} = \dfrac{{z^{8}}}{{z^{-5}a^{2}}}$ Break up the equation by variable and simplify. $\dfrac{{z^{8}}}{{z^{-5}a^{2}}} = \dfrac{{z^{8}}}{{z^{-5}}} \cdot \dfrac{{1}}{{a^{2}}} = z^{{8} - {(-5)}} \cdot a^{- {2}} = z^{13}a^{-2}$.